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58问答库 > 1减去根号下cosx 与4分之x的平方互为等价无穷小吗？为什么？

1减去根号下cosx 与4分之x的平方互为等价无穷小吗？为什么？

2025-03-16 06:39:33

推荐回答（1个）

回答（1）：

等价无穷小是lim（a/b）=0，则ab为等价无穷小为什么在x趋于0时且在相乘关系中可以将1-根号下cosx化简为四分之一x的平方。
在x趋于0时:
1-根号下cosx
=(1-cosx)/（1+根号下cosx）
=1-cosx/2
=1/4x^2 所以为等价无穷小

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